Evaluate this: Cos58/sin32 + sin22/cos68 - …

We have,
{tex}2\left(\frac{\cos58^\circ}{\sin32^\circ}\right)-\sqrt3\left(\frac{\cos38^\circ cosec52^\circ}{\tan15^\circ\tan60^\circ\tan75^\circ}\right){/tex}
{tex}=2\left\{\frac{\cos\left(90^\circ-32^\circ\right)}{\sin32^\circ}\right\}-\sqrt3\left\{\frac{\cos38^\circ cosec\left(90^\circ-38^\circ\right)}{\tan15^\circ\tan60^\circ\tan\left(90^\circ-15^\circ\right)}\right\}{/tex}
{tex}= 2 \left( \frac { \sin 32 ^ { \circ } } { \sin 32 ^ { \circ } } \right) - \sqrt { 3 } \left\{ \frac { \cos 38 ^ { \circ } \sec 38 ^ { \circ } } { \tan 15 ^ { \circ } \times \sqrt { 3 } \times \cot 15 ^ { \circ } } \right\}{/tex}   {tex}\left[\because\;\cos\left(90-\theta\right)=\sin\theta\;,\;\cos ec\left(90-\theta\right)=sec\theta,\;\tan\left(90-\theta\right)=cot\theta\;\right]{/tex}
{tex}= 2 - \sqrt { 3 } \left\{ \frac { \cos 38 ^ { \circ } \times \frac { 1 } { \cos 38 ^ { \circ } } } { \tan 15 ^ { \circ } \times \sqrt { 3 } \times \frac { 1 } { \tan 15 ^ { \circ } } } \right\} = 2 - \frac { \sqrt { 3 } } { \sqrt { 3 } } = 2 - 1 = 1{/tex}    {tex}\left[sec\theta=\frac1{\cos\theta},\;cot\theta=\frac1{\tan\theta}\right]{/tex}

therefore, {tex}2\left(\frac{\cos58^\circ}{\sin32^\circ}\right)-\sqrt3\left(\frac{\cos38^\circ cosec52^\circ}{\tan15^\circ\tan60^\circ\tan75^\circ}\right)=1{/tex}